Holography, chiral Lagrangian and form factor relations

Abstract

We derive all the $ \mathcal{O}\left( {{p^6}} \right) $ Chiral Perturbation Theory low-energy constants from a class of gravity dual models of QCD described by the Yang-Mills and Chern-Simons Lagrangian terms, with the chiral symmetry broken through boundary conditions in the infrared. All the constants of the odd intrinsic parity sector are universally determined by those at $ \mathcal{O}\left( {{p^4}} \right) $ in the even sector, together with an extra resonance term. A few relations for the even sector couplings are also extracted. Our estimates reasonably agree with the few available $ \mathcal{O}\left( {{p^6}} \right) $ determinations from alternative phenomenological analyses. Some of the relations between low-energy constants are the manifestation, at large distances, of universal relations that we find between form factors in the even and odd sectors, e.g., between the γ * → ππ and π → γγ * matrix elements.